runner at first, RHP double-taps front foot: why not a balk?

Not if it's in a "continuous" motion and he repeats it each time from the stretch.  Many pitchers do this where they have a very slight pause between the toe tap before coming set.  So long as they come completely set before their delivery, it isn't a balk.  The toe tap is part of their motion before coming set.

If they come to a complete stop (set), between the tap, then it would be a balk.  Also, if they alternated between tapping and not tapping (intent to deceive), it would also be a balk.

If the pitcher did, in fact, come set before lifting foot and setting it back down as you describe, then I'd be as baffled as you as to why it wouldn't be a balk.

You see more and more toe taps and glove wiggles in the motion of the pitcher coming set.  Probably making it a bit more difficult for umps (who already seemed challenged to recognize a balk when it occurs) to call it.

I didn't look at the GIF but last week when the Blue Jays played the Yankees the TV crew commented on that same question.  I can't recall who was pitching for the Jays but he double tapped every pitch when there was a man on first.  The commentator (I think it was David Cone) said that it's not a balk if that is your normal routine - and you do it every pitch.  I'm not sure why it wouldn't be a balk the first pitch though (as you wouldn't have shown your routine at that point).  

It's what they now call an "adjustment." As mentioned above, as long as you don't completely stop your motion, they won't call it. In reality, it's a balk. Try that in youth ball and see how far you get. You often hear this notion that, if you do it every time, it's just part of your motion. However, there is no rule that supports that interpretation. Balks are clearly defined by rules. If you violate a rule, it's a balk. there's no rule that supports an umpire deciding that "he does it on every pitch, so it's ok," just as there's no rule that says "it's a balk because he attempted to deceive the runner." It's a balk. It's just become customary to allow it.

It actually is written into the MLB rules that the intent of the balk rule is to prevent deception of the baserunner and that the umpire is to consider the intention of the pitcher.  Balks are covered under rule 8.05 and the blurb below is copied directly from the MLB Official Rules.

Rule 8.05 Comment: Umpires should bear in mind that the purpose of the balk rule is to prevent the pitcher from deliberately deceiving the base runner. If there is doubt in the umpire’s mind, the “intent” of the pitcher should govern. However, certain specifics should be borne in mind:
(a) Straddling the pitcher’s rubber without the ball is to be interpreted as intent to deceive and ruled a balk.
(b) With a runner on first base the pitcher may make a complete turn, without hesitating toward first, and throw to second. This is not to be interpreted as throwing to an unoccupied base.

Balks are actually under 6.02(a) now.

And, the "he does it every time" is a myth.

The "intentional deception" is often mis-interpreted.  The pitcher's job is to deceive the runner -- he just must do so legally.

I didn't watch the video / gif, but I do agree that if it's all a continuous motion to come set it should be legal.

While that's true, the comment isn't a rule that can be used. You can't call a balk based exclusively on "deception." It must be a deception that is specifically banned by a balk rule. It is simply a clarification of rules and, here, a simple reminder of why balk rules exist. This particular comment makes no sense. Neither does 8.05(b). That comment is clearly wrong. Throwing to second under such circumstances is clearly, by the rules, "throwing to an unoccupied base." It is, however, an acceptable exception to the prohibition against throwing to an unoccupied bas that is covered by the rule.

I didn't actually watch this particular video, but what I often see is where a pitcher, from the stretch, will set and then tap his foot, bring it back a bit and reset. It's become acceptable at the mlb level as a "readjustment."

Ever see that guy that takes forever to get set?  Starts bringing his hands together around shoulder high and then takes 3-4 seconds while he drops them to his waist where he comes set.  I think the extra step is sort of like that approach.  The key is the you don't stop and sort of keep rocking.  I don't have video, but I have also seen where a pitcher, with his pitching hand/ball inside his glove, will sort of rock his hands - seen this while they are rocking their stance also to include picking up foot.

Probably if you watch that pitcher when he does go to the plate, you will see him do this little dance getting set, will actually get set (i.e. stop moving) and then deliver to the plate.

While we are on the subject, is there any guidance on how a player gets set?  I suppose if they simply keep rocking or gyrating in some fashion so as to never get set, that would be deemed deception and called?

There is absolutely no rule that authorizes an umpire to call a balk on any action that is otherwise not a violation of a specific balk rule solely because he determines it to be an attempt at deception.

Interesting discussion here of "pulsing foot."

https://forum.officiating.com/...er-pulsing-foot.html

To re-state my question:

HS baseball

Runner at first

RHP suspects that r1 may be stealing on this pitch  (he's right!)

RHP comes completely set; his hands are still

He does a long hold, with hands remaining still, then he lifts front foot 1-1.5" off the ground and places it back down in the same place.

Then, about one second later, he wheels and picks to first.

R1 got caught leaning is tagged out diving back to the bag.

For clarification, can someone knowledgeable state what actions a pitcher can legally take once they become set?  My understanding is they have three options.  1 - step and deliver a pitch to the plate, 2 - make a legal throw to a base and 3 - disengage from rubber (at which point all sorts of options open up).

On the restated question, it states that he comes completely set - then moves without disengaging.  This would seem a clear cut balk.  I can only assume the umpire failed to notice the complete set.  The "pulsing foot" seems to be an action that occurs prior to coming set - sort of prolonging the continuous motion.

As described (specifically "completely set" -- it's more than just the hands), that's a balk.  All codes.

Now that I've had a chance to watch the GIF, I can say that the GIF is NOT a balk.  The GIF and the explanation above do not match.

Also, it's very hard to learn about balks by watching MLB.  Even if the rules are the same (and FED does have some differences), there are lots of judgment words in the rules and the way it gets interpreted is different.  As a general statement (with many exceptions, I admit), MLB pitchers don't do the gross moves that FED pitchers do, and MLB umpires are more strict on a lot of the subtle stuff than we would be at all lower levels.

My LHP son has been doing this for a couple years now when in the stretch (same way as the gif above).  Does it every time.  Now I'm not versed on the exact rules/section/numbers on this, but he's never been called for a balk, no one's even brought it up.  Until last year in HS. 

A parent from the other team sitting about 5-10 feet away from me, kept making it a big deal telling his buddy, "that's a balk, that's a balk."  He was quiet at first, till a later inning and he got a little louder.  Ump came over to grab a drink at the fence and I guess he wanted an explanation on why it wasn't a balk.  Ump kept it simple and I remember him saying "he's not set, he's not done with his motion, talk to your coach."  I just thought to myself "fine with me."

And also on that gif above, looked like it was just a pretty good/quick move accompanied by a big lead that got the runner out.